On weighted minihypers in finite projective spaces of square order

Abstract

In [11], weighted $\{\delta(q+1),\delta;k-1,q\}$-minihypers, $q$ square, were characterized as a sum of lines and Baer subgeometries $PG(3,\sqrt{q})$ provided $\delta$ is sufficiently small. We extend this result to a new characterization result on weighted $\{\delta v_{\mu+1},\delta v_{\mu};k-1,q\}$-minihypers. We prove that such minihypers are sums of $\mu$-dimensional subspaces and of (projected) $(2\mu+1)$-dimensional Baer subgeometries.